Title: Simulation and Analysis of Longitudinal Data.
Abstract: Longitudinal data comprise repeated measurements on patients. These measurements can be continuous (e.g. weight) or discrete (e.g. overweight yes or no?). Two classical approaches for statistical analysis of longitudinal data include maximum likelihood estimation, which requires specification of a likelihood to model the distribution of the data, and a semi-parametric approach, which only requires specification of certain components of the likelihood. I will discuss challenges we face in the analysis of longitudinal discrete data and approaches we have taken to overcome these challenges. In particular, I will describe our implementation of a class of first-order antedependence (or Markov) models that induce decaying product correlation structures that are plausible for longitudinal studies. I apply the Markov models in semi-parametric and maximum likelihood based approaches for analysis. In addition, I demonstrate the application of the Markov models for simulating correlated discrete data, which can be helpful when simulating data to compare methods or to assess power in the planning stages of a clinical trial.